A collective brain is what you'd have if human communication prior to the incident associated with the tower of Babel were basically telepathic (which is one interpretation of Julian Jayne's findings), if Jaynes were correct in thinking that consciousness as we know it did not exist 4000 years ago, and if consciousness in those days were basically general rather than individual.

For those who are interested, in a nutshell, the Bicameral Mind was Jaynes' theory that humans prior to around 3000 B.C were essentially only externally-aware in much the same way that other higher animals are. They weren't truly self-aware or conscious in any way that we would understand, and weren't capable of the sort of abstract thought or autobiographical conscious that we take for granted--rather, those people would experience what we think of as "thought" or inspiration as a hallucinatory sort of voice from the portions of their brains that exercised what we think of as metaconscious cognition, and were compelled to obey its commands without any ability to recognize "why" they were doing whatever they were doing, in a manner somewhat akin to that of a modern-day schizophrenic. At some point in the distant past, this state broke down and the human mind completely integrated into what we recognize as a normal conscious state, and the "voices" commanding people to courses of action mostly stopped. This event marked the beginning of what we think of as civilization today.

It's interesting to note that even IF Jaynes' theory is actually true, then it means that what humans thought of as the voices of the gods commanding and compelling men were nothing more than the chatter of the "thinking" portions of their brain telling them what to do, and that the beginnings of most religions are rooted in the struggle of the now fully-self-aware people to bring the voices back.

The Good: Hmm, yes, I suppose a "collective brain" would be pretty much what would result from the situation you describe.
The Bad: Everything leading up to and from that conclusion is batshit crazy spaghetti confetti bananahammock.